\(\frac 2 3+\frac 3 2y+9=0?\)
\(\frac{2x} 3+\frac{3y} 2=-9\)
\(\frac{4x+9y} 6=-9\)
\(4x + 9x = -9 \times 6\)
Divide through by 36
\(\frac{4x}{36}+\frac{9y}{36}=\frac{-9\mathit{X6}}{36}\)
\(\frac x 9+\frac y 4=\frac{-3} 2\)
Multiply through by \(\frac 2 3\)
\(\frac 2 3x\frac x 9+\frac 2 3x\frac y 4=\frac{-3} 2x\frac 2 3\)
\(\frac{2x}{27}+\frac y 6=-1\)
Multiply through by -1
\(\frac{-2x}{27}+\frac y 6=-1\)
The above equation can be written as shown below
\(\frac{-x}{\frac{27} 6}-\frac y 6=1{\dots}{\dots}{\dots}{\dots}.(i)\)
The double intercept form of the equation of a straight line is
\(\frac x a+\frac y b=1{\dots}{\dots}{\dots}{\dots}{\dots}(\mathit{ii})\)
\(a = \frac{-27} 2,b=-6\)
\(a + b = \frac{-27} 2-\frac 6 1\)
\(= \frac{-27-12} 2\)
\(= \frac{-39} 2 = -19.5\)